If you have 100 pounds of potatoes that are 99% water, and they are left in the sun to dry until they are only 98% water, how much will they weigh?

The paradox lies in the unexpected answer, which is 50 pounds.

The potato paradox is a mathematical calculation that has a counter-intuitive result.

Initially, 99 kg of the weight is water, and 1 kg is dry matter. The Ratio Water/DryMatter is therefore 99:1.

If we leave the potatoes dehydrating to 98% water, the 1 kg of dry matter still remains, representing now the 2% of the potatoes. The ratio Water/DryMatter has become, therefore, 98 = 49:1. Thus 49 Kg of water plus 1 kg of dry matter total 50 kg.

So, by reducing the water content by just 1%, the total weight of the potatoes is halved, from 100 kg to 50 kg.

This is the paradox: a small change in the percentage of water leads to a massive change in the total weight.

You have 1 white sock and 99 black socks. If you reduce the amount of black socks to 98% and keep only that 1 white sock, you’ll need to remove enough black ones so the ratio is 1:49 (49/50 black) or 98%. You have to remove 50 black socks for this to happen.

Some time passes, 1kg water evaporates. So total weight: 98kg, total water weight: 97kg so 97 / 98 = 98.97959184% water.

you keep waiting water evaporates more and more.

96kg water / 97 kg total weight = 98.96907216% water.

keep waiting. We calculate water percentage whenever 1kg water evaporates.

95kg water / 96kg total weight = 98.95833333333334% water

94kg water / 95kg total weight = 98.94736842105263% water

93kg water / 94kg total weight = 98.93617021276596% water

92kg water / 93kg total weight = 98.9247311827957% water

91kg water / 92kg total weight = 98.91304347826086% water

90kg water / 91kg total weight = 98.9010989010989% water

89kg water / 90kg total weight = 98.88888888888889% water

88kg water / 89kg total weight = 98.87640449438202% water

87kg water / 88kg total weight = 98.86363636363636% water

86kg water / 87kg total weight = 98.85057471264368% water

85kg water / 86kg total weight = 98.83720930232558% water

84kg water / 85kg total weight = 98.82352941176471% water

83kg water / 84kg total weight = 98.80952380952381% water

82kg water / 83kg total weight = 98.79518072289156% water

81kg water / 82kg total weight = 98.78048780487805% water

80kg water / 81kg total weight = 98.76543209876543% water

79kg water / 80kg total weight = 98.75% water

78kg water / 79kg total weight = 98.73417721518987% water

77kg water / 78kg total weight = 98.71794871794873% water

76kg water / 77kg total weight = 98.7012987012987% water

75kg water / 76kg total weight = 98.68421052631578% water

74kg water / 75kg total weight = 98.66666666666667% water

73kg water / 74kg total weight = 98.64864864864865% water

72kg water / 73kg total weight = 98.63013698630137% water

71kg water / 72kg total weight = 98.61111111111111% water

70kg water / 71kg total weight = 98.59154929577466% water

69kg water / 70kg total weight = 98.57142857142858% water

68kg water / 69kg total weight = 98.55072463768117% water

67kg water / 68kg total weight = 98.52941176470588% water

66kg water / 67kg total weight = 98.50746268656717% water

65kg water / 66kg total weight = 98.48484848484848% water

64kg water / 65kg total weight = 98.46153846153847% water

63kg water / 64kg total weight = 98.4375% water

62kg water / 63kg total weight = 98.4126984126984% water

61kg water / 62kg total weight = 98.38709677419355% water

60kg water / 61kg total weight = 98.36065573770492% water

59kg water / 60kg total weight = 98.33333333333333% water

58kg water / 59kg total weight = 98.30508474576271% water

57kg water / 58kg total weight = 98.27586206896551% water

56kg water / 57kg total weight = 98.24561403508771% water

55kg water / 56kg total weight = 98.21428571428571% water

54kg water / 55kg total weight = 98.18181818181819% water

53kg water / 54kg total weight = 98.14814814814815% water

52kg water / 53kg total weight = 98.11320754716981% water

51kg water / 52kg total weight = 98.07692307692307% water

50kg water / 51kg total weight = 98.0392156862745% water

49kg water / 50kg total weight = 98% water

48kg water / 49kg total weight = 97.95918367346938% water

47kg water / 48kg total weight = 97.91666666666666% water

46kg water / 47kg total weight = 97.87234042553192% water

45kg water / 46kg total weight = 97.82608695652173% water

44kg water / 45kg total weight = 97.77777777777777% water

43kg water / 44kg total weight = 97.72727272727273% water

42kg water / 43kg total weight = 97.67441860465115% water

41kg water / 42kg total weight = 97.61904761904762% water

40kg water / 41kg total weight = 97.5609756097561% water

39kg water / 40kg total weight = 97.5% water

38kg water / 39kg total weight = 97.43589743589743% water

37kg water / 38kg total weight = 97.36842105263158% water

36kg water / 37kg total weight = 97.2972972972973% water

35kg water / 36kg total weight = 97.22222222222221% water

34kg water / 35kg total weight = 97.14285714285714% water

33kg water / 34kg total weight = 97.05882352941177% water

32kg water / 33kg total weight = 96.96969696969697% water

31kg water / 32kg total weight = 96.875% water

30kg water / 31kg total weight = 96.7741935483871% water

29kg water / 30kg total weight = 96.66666666666667% water

28kg water / 29kg total weight = 96.55172413793103% water

27kg water / 28kg total weight = 96.42857142857143% water

26kg water / 27kg total weight = 96.29629629629629% water

25kg water / 26kg total weight = 96.15384615384616% water

24kg water / 25kg total weight = 96% water

23kg water / 24kg total weight = 95.83333333333334% water

22kg water / 23kg total weight = 95.65217391304348% water

21kg water / 22kg total weight = 95.45454545454545% water

20kg water / 21kg total weight = 95.23809523809523% water

19kg water / 20kg total weight = 95% water

18kg water / 19kg total weight = 94.73684210526315% water

17kg water / 18kg total weight = 94.44444444444444% water

16kg water / 17kg total weight = 94.11764705882352% water

15kg water / 16kg total weight = 93.75% water

14kg water / 15kg total weight = 93.33333333333333% water

13kg water / 14kg total weight = 92.85714285714286% water

12kg water / 13kg total weight = 92.3076923076923% water

11kg water / 12kg total weight = 91.66666666666666% water

10kg water / 11kg total weight = 90.9090909090909% water

9kg water / 10kg total weight = 90% water

8kg water / 9kg total weight = 88.88888888888889% water

7kg water / 8kg total weight = 87.5% water

6kg water / 7kg total weight = 85.71428571428571% water

5kg water / 6kg total weight = 83.33333333333334% water

4kg water / 5kg total weight = 80% water

3kg water / 4kg total weight = 75% water

2kg water / 3kg total weight = 66.66666666666666% water

1kg water / 2kg total weight = 50% water